The quantum mutual entropy was introduced by one of the present authors in 1983 as a quantum extension of the Shannon mutual information. It has been used for several studies such as quantum information transmission in optical communication and quantum irreversible processes. In this paper, a nonlinear channel for a quantum teleportation process is rigorously constructed and the quantum mutual ...

We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A.A. Brudno [2]. On the other hand, using the quantu...

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality a...

The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that the classical-quantum correspondences such as encodings can be treated as diagonal (d-) entanglements. The mutual entropy of the d-compound and entangled states lead to two different types of entropies for a given quantum state: the von Neumann entropy, wh...

We consider the extremal limit of a black hole geometry of the Reissner-Nordstrom type and compute the quantum corrections to its entropy. Universally, the limiting geometry is the direct product of two 2-dimensional spaces and is characterized by just a few parameters. We argue that the quantum corrections to the entropy of such extremal black holes due to a massless scalar field have a univer...

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a mixed density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy ...